Lattice field theory is the most direct, first principle
way to approach non-perturbative dynamics.
Detailed lattice studies of theories leading to symmetry breaking described by the
\(SU(4)/Sp(4)\sim SO(6)/SO(5)\)  coset have focused on the simplest \(SU(2)\)  gauge theories
coupled to fundamental fermions [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, but these models cannot realise top compositeness.
Explorations of \(SU(4)\)  gauge theories with multiple representations [10]}, [11]}, [12]}, [13]}, [14]}, [15]} aim at
gathering non-perturbative information about Ferretti's \(SU(5)/SO(5)\) 
model [16]}, though
the fermionic field contents do not match.
An alternative route to studying models yielding both composite Higgs and partial top compositeness
has been proposed by Vecchi in Ref. [17]} (see also
Refs. [18]}, [19]}), by exploiting the fact that in \(SU(3)\)  theories
the antisymmetric representation is the conjugate of the fundamental,
so that one can use the lattice information made available over the years by the
LatKMI [20]}, [21]} and LSD [22]}, [23]}, [24]} collaborations
to test the viability of CHMs based on the \(SU(N_f)\times SU(N_f)/SU(N_f)\)  cosets
(as done explicitly in Ref. [25]}).
